Formulas for the multiplicity of graded algebras
Abstract
Let R be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of R by means of local j-multiplicities of various hyperplane sections. This formula yields the multiplicity of A in terms of that of B and of local j-multiplicities of hyperplane sections along Proj (B) when applied to a homogeneous inclusion A ⊆ B of standard graded Noetherian algebras over an Artinian local ring. Our formulas can be used to find the multiplicity of special fiber rings and to obtain a generalization of Teissier’s Plücker formula to hypersurfaces with non-isolated singularities. We also discuss some special cases and obtain simpler formulas. Our work generalizes results by Simis, Ulrich and Vasconcelos about homogeneous embeddings of graded algebras.
Degree
Ph.D.
Advisors
Ulrich, Purdue University.
Subject Area
Mathematics
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